Work And Energy: Learning objectives
At the end of this chapter the students will be able to:

  1. Understand the concept of work in terms of the product of a force and displacement in the direction of the force.
  2. Understand and derive the formula work = wd = mgh for work done in a gravitational field near Earth’s surface
  3. Understand that work can be calculated from area under the force-displacement graph.
  4. Relate power to work done.
  5. Define power as the product of force and velocity.
  6. Quote examples of power from everyday life.
  7. Explain the two types of mechanical energy.
  8. Understand the work-energy principle.
  9. Derive an expression for absolute potential energy.
  10. Define escape velocity.
  11. Understand that in a resistive medium loss of potential energy of a body is equal to gain in kinetic energy of the body plus work done by the body against friction.
  12. Give examples of conservation of energies from everyday life.
  13. Describe some non-conventional sources of energy.

Work is often thought in terms of physical or mental effort. In physics, however , the term work involves two things (i) force (ii) displacement . we shall begin with a simple situation in which work is done by a constant force.

4.1 work done by a constant force

Let us consider an object which is being pulled by a constant force F at an angle θ to the direction of motion. The force displaces the object from position A to B through a displacement d (Fig. 4.1).

constant_force

Fig. 4.1

We define work W done by the force F as the scalar product of F and d.

W = F.d = Fd cos θ            ………….                 (4.1)

= (F cosθ) d

The quantity (F cosθ) is the component of the force in the direction of the displacement d.

The , the work done on a body by a constant force is defined as the product of the magnitudes of the displacement and the component of the force in the direction of the displacement.

Can you tell how much work is being done?

(i)                  One the pail when a person holding the pail by the force F is moving forward (Fig. 4.2 a).

force-F-is-moving

Fig. 4.2 (a)

(ii)                On the wall (Fig. 4.2 b)?

On_the_wall

Fig. 4.2 (b)

When a constant force acts through a distance d, the event can be plotted on a simple graph (fig. 4.3). the distance is normally plotted along x-axis and the force along y-axis. In this case as the force does not vary, the graph will be a horizontal straight line, if the constant force F (newton) and the displacement d (metre) are in the same direction then the work done is Fd (joule). Clearly shaded area in fig. 4.3 is also Fd. Hence the area under a force- displacement curve can be taken to represent the work done by the force. In case the force F is not in the direction of displacement, the graph is plotted between F cos θ and d.

From the definition of work, we find that:

(i)                  Work is a scalar quantity.

(ii)                If θ < 90⁰, work is done and it is said to be positive work.

(iii)               If θ = 90⁰, no work is done.

(iv)              If θ > 90⁰, the work done is said to be negative.

(v)                SI unit of work is N m known as joule (J).